Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Let I⊆R=K[x1,…,xn] be a toric ideal, i.e., binomial prime ideal. We investigate when the ideal I can “split” into sum of two smaller ideals. For general I, we give sufficient condition for this splitting in terms integer matrix that defines I. When I=IG is finite simple graph G, additional splittings IG related to subgraphs G. there exists I=I1+I2 show some cases describe (multi-)graded Betti n...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

One should be cautious in using long term tetracyclines, thiazides or steroids during pregnancy.  In toxemic pregnant patients who are com­plaining of epigastric pains, pancreatitis should be ruled qu t. Two patients who developed pancreatitis during their pregnancy are introduced and the dilemma of diagnosing this process from other causes of acute abdomen are discussed. It is suggested not t...

Due to its constantly growing incidence, obesity is an increasingly serious social and medical problem. Available data on the use of novel oral anticoagulants in morbidly obese and obese patients are very limited. However, we tried to summarize the available knowledge on the use of anticoagulants in this subpopulation of patients in everyday clinical practice. Studies on the clinical use of ant...

OBJECTIVE To evaluate the current and ideal body weight perceptions of schoolchildren in relation to their actual body weight and socio-economic status (SES). DESIGN Baseline evaluation of schoolchildren from January 2008 to April 2008 as part of a 3-year longitudinal study. SETTING City and non-city locations, Karnataka State, South India. SUBJECTS Schoolchildren (n 1877) aged between 8 ...

Although the burgeoning discipline of welfare economics is based on essentially utilititarian principles, the foundations of utilitarianism have received little attention in recent years. This paper seeks to reopen the debate by drawing a distinction between Harsanyi’s two defences of utilitarianism, labeling the first a teleological or ideal-observer theory, and the second a nonteleological th...